On the Classification of Stable Rank-r Vector Bundles over the Projective Plane

1980 ◽  
pp. 113-144 ◽  
Author(s):  
Klaus Hulek
Keyword(s):  
Projective Plane ◽  
Vector Bundles ◽  
Stable Rank

scholarly journals Generalized null correlation bundles

1988 ◽  
Vol 111 ◽  
pp. 13-24 ◽  
Author(s):  
Lawrence Ein
Keyword(s):  
Moduli Space ◽  
Vector Bundles ◽  
Topological Type ◽  
Stable Rank ◽  
Chern Classes ◽  
Smooth Variety ◽  
Rank 2 ◽  
Rank 2 Vector Bundles

It is well known that the moduli space of stable rank 2 vector bundles on ℙ2 of the fixed topological type is an irreducible smooth variety ([1], and [8]). There are also many known results on the classification of stable rank 2 vector bundles on ℙ3 with “small” Chern classes.

scholarly journals Fano 3-folds from homogeneous vector bundles over Grassmannians

2021 ◽  
Author(s):  
Lorenzo De Biase ◽  
Enrico Fatighenti ◽  
Fabio Tanturri
Keyword(s):  
Vector Bundles ◽  
Homogeneous Vector

AbstractWe rework the Mori–Mukai classification of Fano 3-folds, by describing each of the 105 families via biregular models as zero loci of general global sections of homogeneous vector bundles over products of Grassmannians.

scholarly journals Two-Categorical Bundles and their Classifying Spaces

2012 ◽  
Vol 10 (2) ◽  
pp. 299-369 ◽  
Author(s):  
Nils A. Baas ◽  
Marcel Bökstedt ◽  
Tore August Kro
Keyword(s):  
Vector Bundle ◽  
Vector Bundles ◽  
Vector Spaces ◽  
Bundle Theory ◽  
Classifying Spaces ◽  
Classifying Space ◽  
Principal Bundles

AbstractFor a 2-category 2C we associate a notion of a principal 2C-bundle. For the 2-category of 2-vector spaces, in the sense of M.M. Kapranov and V.A. Voevodsky, this gives the 2-vector bundles of N.A. Baas, B.I. Dundas and J. Rognes. Our main result says that the geometric nerve of a good 2-category is a classifying space for the associated principal 2-bundles. In the process of proving this we develop powerful machinery which may be useful in further studies of 2-categorical topology. As a corollary we get a new proof of the classification of principal bundles. Another 2-category of 2-vector spaces has been proposed by J.C. Baez and A.S. Crans. A calculation using our main theorem shows that in this case the theory of principal 2-bundles splits, up to concordance, as two copies of ordinary vector bundle theory. When 2C is a cobordism type 2-category we get a new notion of cobordism-bundles which turns out to be classified by the Madsen–Weiss spaces.

Cohomology of Homotopy 2-types

2019 ◽  
pp. 379-422
Author(s):  
Graham Ellis
Keyword(s):  
Perturbation Theory ◽  
Projective Plane ◽  
Integral Homology ◽  
Homotopy Classes ◽  
Cw Complex ◽  
Crossed Modules ◽  
Homological Perturbation Theory ◽  
Homological Perturbation ◽  
Manual Classification

This chapter introduces some of the basic ingredients in the classification of homotopy 2-types and describes datatypes and algorithms for implementing them on a computer. These are illustrated using computer examples involving: the fundamental crossed modules of a CW-complex, cat-1-groups, simplicial groups, Moore complexes, the Dold-Kan correspondence, integral homology of simplicial groups, homological perturbation theory. A manual classification of homotopy classes of maps from a surface to the projective plane is also included.

scholarly journals The group structure of the homotopy set whose target is the automorphism group of the Cuntz algebra

2019 ◽  
Vol 30 (11) ◽  
pp. 1950057 ◽  
Author(s):  
M. Izumi ◽  
T. Sogabe
Keyword(s):  
Automorphism Group ◽  
Vector Bundles ◽  
Group Structure ◽  
Cuntz Algebra ◽  
Classifying Space ◽  
Cuntz Algebras ◽  
K Theory ◽  
Continuous Fields

We determine the group structure of the homotopy set whose target is the automorphism group of the Cuntz algebra [Formula: see text] for finite [Formula: see text] in terms of K-theory. We show that there is an example of a space for which the homotopy set is a noncommutative group, and hence, the classifying space of the automorphism group of the Cuntz algebra for finite [Formula: see text] is not an H-space. We also make an improvement of Dadarlat’s classification of continuous fields of the Cuntz algebras in terms of vector bundles.

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